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Interpretability and Optimality

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2091)

Abstract

The Semantic Theorems show that \({f}^{{\ast}}(\boldsymbol{X})\) and \({f}^{{\ast}{\ast}}(\boldsymbol{X})\) are optimal from a semantic point of view, and clarify which ⊆ -sense of rounding is the right one when *-semantic or **-semantic are to be applied. They provide, therefore, a general norm that computational functions F from \({I}^{{\ast}}({\mathbb{R}}^{k})\) to \({I}^{{\ast}}(\mathbb{R})\) must satisfy to conform to the f or the f ∗∗-semantic, but this is still not a general procedure by which these functions may be effectively computed. These procedures will be provided by the modal syntactic extension of continuous real functions, as far as they satisfy certain suitability conditions.

Keywords

  • Logical Formula
  • Modal Interval
  • Existential Quantifier
  • Continuous Real Function
  • Semantic Point

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. P. Thieler, Technical calculations by means of interval mathematics (1985), pp. 197–208

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© 2014 Springer International Publishing Switzerland

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Sainz, M.A., Armengol, J., Calm, R., Herrero, P., Jorba, L., Vehi, J. (2014). Interpretability and Optimality. In: Modal Interval Analysis. Lecture Notes in Mathematics, vol 2091. Springer, Cham. https://doi.org/10.1007/978-3-319-01721-1_4

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